Theorems · Theorem · real analysis

derivWithin_clm_apply

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {x : 𝕜} {s : Set 𝕜} {G : Type u_2} [inst_3 : NormedAddCommGroup G]
  [inst_4 : NormedSpace 𝕜 G] {c : 𝕜 → F →L[𝕜] G} {u : 𝕜 → F},
  DifferentiableWithinAt 𝕜 c s x →
    DifferentiableWithinAt 𝕜 u s x →
      derivWithin (fun y => (c y) (u y)) s x = (derivWithin c s x) (u x) + (c x) (derivWithin u s x)

Defined in

Mathlib.Analysis.Calculus.Deriv.Mul

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace